On our trip the week after Easter almost all of our actual waits were less than or equal to the posted wait times. In some cases, the actual waits were significantly lower than the posted waits.
The most notable exception was when we entered the single rider line at about 8:45 on a day with an 8 AM EMH. Because of some issues with our bus from WLV to Epcot (the main issue was with the stop at Fort Wilderness at a couple of scooters that had to be loaded, we didn't get to Epcot as early as we wanted, and it took us longer to ride Soarin than it would have if we had arrived at 7:30-7:40 like we should have. Anyway, when we got to TT the posted wait for single rider, the posted time was 25 minutes, but the line was out the building, leading us to suspect that the wait would be longer. But, because it was going to be a crowd level 10 day at Epcot, we decided to wait because we didn't have any other priority attractions that morning. Not long after we got in line, someone behind us said the posted wait had just gone up to 45 minutes, and our wait ended up being about 35-40.
The moral of the story is something that we learned years ago. The posted wait times at the most popular attractions can be very inaccurate in the first hour or so after opening. They start high to account for the anticipated initial surge, and then get bumped up as the surge occurs. At 7DMT for example, we were in the first wave to arrive and the posted wait time was 45 minutes even though we were on and off in less than 10 minutes. When we got off, the posted wait was still 45 minutes, which may or may not have been accurate by then.
In the case of the OP's experience, if there was no ride breakdown, you probably got caught in the gap between the initial surge and the posted wait time being bumped up to account for the crowd having built up past the earlier posted time. The posted time was probably increased shortly after you entered the line.